Independently of the above, we also point out that the results obtained in [1]} cannot be extrapolated to the anti-D3-brane uplift in the KKLT construction [2]}. The reason is the following shortcoming stated at the end of the introduction in [1]}: light states surviving in the IR can disrupt their procedure. Given that the SUSY breaking scale for the anti-D3-brane in the KKLT scenario is the warped down string scale, which is above the warped down KK scale, there are plenty of light fields below the SUSY breaking scale. In particular, the world volume fields on the anti-D3-brane contain in addition to the goldstino a massless U(1) gauge field. Such light fields have been neglected in the analysis of [1]}. We will discuss below in section  explicit examples where the presence of light states ensures the absence of potential instabilities and we argue that this should also apply to the anti-D3-brane in KKLT.
